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- W2079430060 abstract "We study undirected networks with edge costs that satisfy the triangle inequality. Let n denote the number of nodes. We present an $O(1)$-approximation algorithm for a generalization of the metric-cost subset k-node-connectivity problem. Our approximation guarantee is proved via lower bounds that apply to the simple edge-connectivity version of the problem, where the requirements are for edge-disjoint paths rather than for openly node-disjoint paths. A corollary is that, for metric costs and for each $k=1,2,dots,n-1$, there exists a k-node connected graph whose cost is within a factor of ${ 22/}$ of the cost of any simple k-edge connected graph. Based on our $O(1)$-approximation algorithm, we present an $O(log r_{max})$-approximation algorithm for the metric-cost node-connectivity survivable network design problem, where $r_{max}$ denotes the maximum requirement over all pairs of nodes. Our results contrast with the case of edge costs of 0 or 1, where Kortsarz, Krauthgamer, and Lee. [SIAM J. Comput., 33 (2004), pp. 704–720] recently proved, assuming NP$nsubseteq;$DTIME($n^{polylog(n)}$), a hardness-of-approximation lower bound of $2^{log^{1-epsilon}n}$ for the subset k-node-connectivity problem, where $epsilon$ denotes a small positive number." @default.
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- W2079430060 date "2007-01-01" @default.
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- W2079430060 title "Approximation Algorithms for Network Design with Metric Costs" @default.
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- W2079430060 doi "https://doi.org/10.1137/040621806" @default.
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